Microstate counting from defects in de Sitter

TL;DR

This paper investigates the microscopic origin of de Sitter entropy using a Lorentzian path-integral approach, constructing a Hilbert space from shell and brane configurations, and finds that wormhole topologies dominate microstate overlaps, reproducing the area law.

Contribution

It introduces a novel Lorentzian path-integral framework to derive de Sitter entropy from microstate overlaps involving wormhole topologies and extends the analysis to Schwarzschild-de Sitter spacetime.

Findings

Reproduces the area law for de Sitter entropy from microstate overlaps.

Shows both cosmological and black hole horizons contribute to entropy.

Constructs explicit shell and brane configurations consistent with energy conditions.

Abstract

We explore the microscopic origin of de Sitter entropy using a Lorentzian path-integral approach. We construct a Hilbert space whose states are associated with configurations of thin shells or end-of-the-world branes, with state overlaps defined by the gravitational path integral. By considering states which are indistinguishable to an observer, we find that the variance of microstate overlaps is dominated by Lorentzian wormhole topologies with conical singularities. Evaluating these overlaps, we recover the expected area law for the entropy, relating the dimension of the de Sitter Hilbert space to the area of the cosmological horizon. Extending this analysis to Schwarzschild-de Sitter spacetime, we show that both the cosmological and black hole horizons contribute to the total entropy. Along the way, we present an explicit construction of the shell and brane configurations and examine their compatibility with relevant consistency conditions, including the null energy condition.